1.075 as a fraction
Understand the Problem
The question is asking how to convert the decimal 1.075 into a fraction. This involves expressing the decimal in terms of its simplest fractional form, which can be done by identifying the whole number part and the fractional part separately, and then combining them appropriately.
Answer
$\frac{43}{40}$
Answer for screen readers
The decimal 1.075 can be expressed as the fraction $\frac{43}{40}$.
Steps to Solve
- Identify Whole and Fractional Parts
The decimal number 1.075 has a whole part (1) and a fractional part (0.075).
- Convert the Fractional Part to a Fraction
To convert the fractional part, we can express 0.075 as $\frac{75}{1000}$. This is because there are three decimal places, which means we can think of 0.075 as $\frac{75}{1000}$.
- Simplify the Fraction
Next, we simplify $\frac{75}{1000}$. We can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 75 and 1000 is 25, so we divide both:
$$ \frac{75 \div 25}{1000 \div 25} = \frac{3}{40} $$
- Combine the Whole and Fractional Parts
Now we can combine the whole number and the simplified fraction. We can express the whole number 1 as $\frac{40}{40}$ to have a common denominator:
$$ 1 = \frac{40}{40} $$
- Add the Fractions
Now, we can add the two fractions:
$$ \frac{40}{40} + \frac{3}{40} = \frac{40 + 3}{40} = \frac{43}{40} $$
The decimal 1.075 can be expressed as the fraction $\frac{43}{40}$.
More Information
The fraction $\frac{43}{40}$ is an improper fraction, meaning the numerator is greater than the denominator. This shows that the decimal is slightly greater than 1.
Tips
- Forgetting to convert the decimal part correctly, leading to an incorrect fraction.
- Not simplifying the fraction before combining it with the whole number.
- Misadding fractions with different denominators.
